defines a smooth function where so I am guessing it is a unit sphere.
How do we proceed with such problem?
f is a smooth function if all partial derivatives of all possible orders are defined in all points of the domain of f right?
I started with computing these partial derivatives
and these partial derivatives are all defined at any point from the domain of f
so I compute second order partial derivatives
and these 3 are also defined for all the points of the domain.
if I continue differentiating
which is defined for all points
What should I do next? can I conclude based on the calculations that f is certainly smooth?
Thanks in advance